24-Bld-A6 Geotechnical Materials and Analysis · May 2018
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.
In this classical analogy, the spring represents the compressible soil skeleton (the mineral particle structure that ultimately carries the effective stress), the water in the cylinder represents the pore water, and the small valve at the top of the piston represents the soil's permeability — how readily water can escape the void spaces.
Stage 1 (equilibrium, no load): before any load is applied, the spring carries only its own initial compression and the water pressure is simply hydrostatic; there is no excess pore pressure and no tendency for flow — this mirrors an undisturbed clay layer at its existing effective overburden stress.
Stage 2 (Δσ applied, valve closed): the moment the load $\Delta\sigma$ is applied, the valve is still closed (no drainage has occurred yet, representing clay's low permeability at $t=0^+$). Because water is essentially incompressible and cannot yet escape, the piston cannot move, so the spring cannot compress — the *entire* applied stress increment is carried by the water as excess pore pressure, $\Delta u=\Delta\sigma$, and the effective stress on the spring is unchanged. This is the "undrained" instant of loading.
Stage 3 (valve open, water draining): once the valve opens (representing the finite time needed for water to migrate through the clay's pores under the excess head), water begins to escape and the piston moves down. As it moves, the spring compresses and starts to pick up load, so the effective stress rises while the excess pore pressure $\Delta u$ decays correspondingly — at every instant, $\Delta\sigma=\Delta\sigma'+\Delta u$ (Terzaghi's principle in the analogy). This transient stage is the actual "consolidation" process: settlement is *time-dependent* because it is throttled by how fast water can escape (the size of the valve opening / the permeability), not by the magnitude of the load alone.
Stage 4 (equilibrium under Δσ): once drainage is complete, the excess pore pressure has fully dissipated ($\Delta u\to0$) and the spring alone now carries the entire applied stress increment ($\Delta\sigma'=\Delta\sigma$). The piston has reached its new equilibrium position, corresponding to the clay layer having reached its final (100%) primary consolidation settlement.
